apologies Don.   I don't have my original cd's and tapes and am getting my info from tapes I made for traveling music in my car. I remembered after my last post that I miss-labeled some of those tapes.
"That Yodeling Song" is different than the "Happy Yodeler"....and you're right that Bill recorded "That Yodeling Song". I went through the songs on my tapes and believe that the song you're looking for is on his "Rodeo Rose" cassette. Couldn't find the cassette listed at Folk-Legacy.

(thanks "el joeclone" for fixing my link)